Exponential Command

Exponential( <Lambda>, <Variable Value> ): Calculates the value of the cumulative distribution function of an Exponential distribution at variable value v, i.e. the probability P(X ≤ v) where X is a random variable with an Exponential distribution defined by the parameter lambda.

This syntax returns the probability at a given value, that is the area under the Exponential distribution curve to the left of the given x-coordinate.

Exponential( <Lambda>, <Variable Value>, <Boolean Cumulative> ): If Cumulative = true, calculates the value of the cumulative distribution function of an Exponential distribution with given lambda parameter at the given variable value, otherwise it calculates the probability density function of the distribution at variable value.
Exponential( <Lambda>, x, <Boolean Cumulative> ): If Cumulative = true, creates the cumulative density function (cdf) of an Exponential distribution with given lambda, othewise it creates the probability density function (pdf) of the distribution.

CAS Syntax

Exponential( <Lambda>, <Variable Value> ): Calculates the value of the cumulative distribution function of an Exponential distribution at variable value v, i.e. the probability P(X ≤ v) where X is a random variable with Exponential distribution with parameter lambda.

Exponential(2, 1) yields \(1 - \frac{1}{e^{2} } \), which is approximately 0.86.